A lift is raised by a cable on a 1.0m diameter pulley-wheel. Assuming that the p

Question

A lift is raised by a cable on a 1.0m diameter pulley-wheel. Assuming that the pulley-wheel starts from rest and accelerates with a uniform rate of 0.3 rad's 2 for 12s, calculate, The speed of the lift in mph at the end of the 12s The distance the lift has moved in the 12s If the lift tackle weight 2 metric tons, while the pulley wheel weighs 75kg, find the power required raise the lift in part b, Assume that the pulley-wheel is a solid wheel is a solid wheel and that there are no losses due to frictional forces.

Explanation / Answer

pulley wheel: radius r = 0.5 m, mass m = 75 kg

mass of lift and tackle M = 2000 kg

angular acceleration = 0.3 rad/s2

time t = 12 s

a) v = r = (t)r = 1.8 m/s

b) d= (0 + v)*t/2 = 10.8 m

c) energy E = Mv2/2 +I2/2 = Mv2/2 + (mr2/2)2/2 = (M + m/2)v2/2 = 3.30 kJ

power = E/t = 0.275 kW

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